Group #11793125 — subgroups

Subgroups — #11793125

Order 1152.

417 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 417 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#63365	C₂	1	3	yes	maximal
3	#10588204	C₂	1	3	yes	maximal, complemented
4	#71896	—	3	1	no	maximal
5	C₂²×#611	C₂²	1	1	yes	characteristic
6	C₉×C₂²⋊Q₈	—	2	6	no	—
7	C₂×C₉×C₂²⋊C₄	C₂²	1	3	yes	—
8	C₂×#3676	C₂²	1	3	yes	—
9	#63365	—	2	6	no	—
10	C₃×#543	D₃	1	1	yes	characteristic
11	C₂×#806	—	3	3	no	—
12	#4527	—	3	3	no	—
13	C₂⁴×C₉	C₂³	1	1	yes	characteristic
14	C₂³×D₉	Q₈	1	1	yes	characteristic, complemented
15	C₂×Q₈×C₉	—	2	2	no	—
16	C₂²×C₄×C₉	—	2	3	no	—
17	C₂×#611	—	2	3	no	—
18	C₂×#611	—	2	3	no	—
19	C₂²×Dic₉	—	2	3	no	—
20	C₂²×Dic₉	Q₈	1	1	yes	characteristic, complemented
21	C₉×C₄⋊C₄	—	2	6	no	—
22	C₉×C₂²⋊C₄	—	2	3	no	—
23	C₉×C₂²⋊C₄	D₄	1	6	yes	—
24	#3676	—	2	3	no	—
25	#3676	—	2	3	no	—
26	#2032	—	9	1	no	Sylow
27	C₂²×#67	—	3	1	no	—
28	C₃×C₂²⋊Q₈	—	2	6	no	—
29	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	3	yes	—
30	C₂×#217	—	3	3	no	—
31	#806	—	6	6	no	—
32	C₂³×C₉	—	8	1	no	—
33	C₂³×C₉	C₂×D₄	1	3	yes	—
34	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
35	C₂³×C₉	#41	1	3	yes	—
36	C₂²×D₉	—	2	3	no	—
37	C₂²×D₉	—	8	1	no	—
38	Q₈×C₉	—	8	2	no	—
39	C₂×C₄×C₉	—	2	6	no	—
40	C₂×C₄×C₉	—	8	3	no	—
41	#611	—	4	1	no	—
42	#611	—	4	3	no	—
43	C₂×Dic₉	—	2	3	no	—
44	C₂×Dic₉	—	4	3	no	—
45	C₂×Dic₉	—	8	3	no	—
46	#543	D₉	1	1	yes	characteristic, complemented
47	C₂×#99	—	9	3	no	—
48	#342	—	9	3	no	—
49	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
50	C₂³×D₃	—	3	1	no	—
51	C₂×C₃×Q₈	—	2	2	no	—
52	C₂²×C₃×C₄	—	2	3	no	—
53	C₂×#67	—	6	3	no	—
54	C₂×#67	—	6	3	no	—
55	C₂²×Dic₃	—	3	1	no	—
56	C₂²×Dic₃	—	6	3	no	—
57	C₃×C₄⋊C₄	—	2	6	no	—
58	C₃×C₂²⋊C₄	—	2	3	no	—
59	C₃×C₂²⋊C₄	#67	1	6	yes	—
60	#217	—	6	3	no	—
61	#217	—	6	3	no	—
62	C₂²×C₉	—	4	3	no	—
63	C₂²×C₉	—	4	3	no	—
64	C₂²×C₉	—	4	1	no	—
65	C₂²×C₉	#120	1	1	yes	characteristic
66	C₂²×C₉	C₂²⋊Q₈	1	3	yes	—
67	C₂²×C₉	#124	1	3	yes	—
68	C₂×D₉	—	4	1	no	—
69	C₂×D₉	—	8	3	no	—
70	C₄×C₉	—	4	6	no	—
71	Dic₉	—	4	1	no	—
72	Dic₉	—	8	3	no	—
73	C₂²×D₄	—	9	1	no	—
74	C₂²⋊Q₈	—	2	6	no	—
75	C₂×C₂²⋊C₄	—	9	3	no	—
76	C₂×C₂²⋊C₄	C₂×D₉	1	3	yes	—
77	#99	—	18	6	no	—
78	C₂³×C₃	—	8	1	no	—
79	C₂³×C₃	D₃×Q₈	1	1	yes	characteristic
80	C₂³×C₃	#239	1	3	yes	—
81	C₂³×C₃	C₂×#67	1	3	yes	—
82	C₂²×D₃	—	6	3	no	—
83	C₂²×D₃	—	24	1	no	—
84	C₃×Q₈	—	8	2	no	—
85	C₂×C₃×C₄	—	2	6	no	—
86	C₂×C₃×C₄	—	8	3	no	—
87	#67	—	12	3	no	—
88	#67	—	12	1	no	—
89	C₂×Dic₃	—	6	3	no	—
90	C₂×Dic₃	—	12	3	no	—
91	C₂×Dic₃	—	24	3	no	—
92	C₂×C₉	—	2	3	no	—
93	C₂×C₉	—	2	1	no	—
94	C₂×C₉	—	2	3	no	—
95	C₂×C₉	#393	1	1	yes	characteristic
96	D₉	—	8	1	no	—
97	C₂⁴	—	9	1	no	—
98	C₂⁴	C₂²×D₉	1	1	yes	characteristic
99	C₂×Q₈	—	2	2	no	—
100	C₂×D₄	—	18	3	no	—
101	C₂×D₄	—	18	3	no	—
102	C₂²×C₄	—	2	3	no	—
103	C₂²×C₄	—	9	1	no	—
104	C₂²×C₄	—	18	3	no	—
105	C₄⋊C₄	—	2	6	no	—
106	C₂²⋊C₄	—	2	3	no	—
107	C₂²⋊C₄	—	18	3	no	—
108	C₂²⋊C₄	—	18	3	no	—
109	C₂²⋊C₄	#611	1	6	yes	—
110	C₂²×C₃	—	4	3	no	—
111	C₂²×C₃	—	4	3	no	—
112	C₂²×C₃	—	4	1	no	—
113	C₂²×C₃	#946	1	3	yes	—
114	C₂²×C₃	#947	1	3	yes	—
115	C₂²×C₃	#953	1	1	yes	characteristic
116	C₂×D₃	—	12	1	no	—
117	C₂×D₃	—	24	3	no	—
118	C₃×C₄	—	4	6	no	—
119	Dic₃	—	12	1	no	—
120	Dic₃	—	24	3	no	—
121	C₉	#2032	1	1	yes	characteristic, complemented, Sylow
122	C₂³	—	8	1	no	—
123	C₂³	—	18	3	no	—
124	C₂³	—	72	1	no	—
125	C₂³	Q₈×D₉	1	1	yes	characteristic
126	C₂³	#3701	1	3	yes	—
127	C₂³	C₂×#611	1	3	yes	—
128	Q₈	—	8	2	no	—
129	D₄	—	36	3	no	—
130	D₄	—	36	1	no	—
131	C₂×C₄	—	2	6	no	—
132	C₂×C₄	—	8	3	no	—
133	C₂×C₄	—	18	3	no	—
134	C₂×C₄	—	36	3	no	—
135	C₂×C₄	—	72	3	no	—
136	C₂×C₃	—	2	3	no	—
137	C₂×C₃	—	2	1	no	—
138	C₂×C₃	—	2	3	no	—
139	C₂×C₃	#5231	1	1	yes	characteristic
140	D₃	—	24	1	no	—
141	C₂²	—	4	3	no	—
142	C₂²	—	4	3	no	—
143	C₂²	—	4	1	no	—
144	C₂²	—	36	1	no	—
145	C₂²	—	72	3	no	—
146	C₂²	#63508	1	3	yes	—
147	C₂²	#63509	1	3	yes	—
148	C₂²	#63515	1	1	yes	characteristic
149	C₄	—	4	6	no	—
150	C₄	—	36	1	no	—
151	C₄	—	72	3	no	—
152	C₃	#71896	1	1	yes	characteristic
153	C₂	—	2	1	no	—
154	C₂	—	2	3	no	—
155	C₂	—	2	3	no	—
156	C₂	—	72	1	no	—
157	C₂	#10588911	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#543

C₂

yes

maximal, characteristic, complemented

C₂×#63365

C₂

yes

maximal

#10588204

C₂

yes

maximal, complemented

#71896

—

maximal

C₂²×#611

C₂²

yes

characteristic

C₉×C₂²⋊Q₈

—

C₂×C₉×C₂²⋊C₄

C₂²

yes

—

C₂×#3676

C₂²

yes

—

#63365

—

C₃×#543

D₃

yes

characteristic

C₂×#806

—

#4527

—

C₂⁴×C₉

C₂³

yes

characteristic

C₂³×D₉

Q₈

yes

characteristic, complemented

C₂×Q₈×C₉

—

C₂²×C₄×C₉

—

C₂×#611

—

C₂×#611

—

C₂²×Dic₉

—

C₂²×Dic₉

Q₈

yes

characteristic, complemented

C₉×C₄⋊C₄

—

C₉×C₂²⋊C₄

—

C₉×C₂²⋊C₄

D₄

yes

—

—

—

—

C₂²×#67

—

C₃×C₂²⋊Q₈

—

C₂×C₃×C₂²⋊C₄

C₂×D₃

yes

—

C₂×#217

—

#806

—

C₂³×C₉

—

C₂³×C₉

C₂×D₄

yes

—

C₂³×C₉

C₂×Q₈

yes

characteristic

C₂³×C₉

#41

yes

—

C₂²×D₉

—

C₂²×D₉

—

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

#611

—

#611

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

#543

D₉

yes

characteristic, complemented

C₂×#99

—

#342

—

C₂⁴×C₃

C₂²×D₃

yes

characteristic

C₂³×D₃

—

C₂×C₃×Q₈

—

C₂²×C₃×C₄

—

C₂×#67

—

C₂×#67

—

C₂²×Dic₃

—

C₂²×Dic₃

—

C₃×C₄⋊C₄

—

C₃×C₂²⋊C₄

—

C₃×C₂²⋊C₄

#67

yes

—

#217

—

#217

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

#120

yes

characteristic

C₂²×C₉

C₂²⋊Q₈

yes

—

C₂²×C₉

#124

yes

—

C₂×D₉

—

C₂×D₉

—

C₄×C₉

—

Dic₉

—

Dic₉

—

C₂²×D₄

—

C₂²⋊Q₈

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₉

yes

—

#99

—

C₂³×C₃

—

C₂³×C₃

D₃×Q₈

yes

characteristic

C₂³×C₃

#239

yes

—

C₂³×C₃

C₂×#67

yes

—

C₂²×D₃

—

C₂²×D₃

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

#67

—

#67

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

#393

yes

characteristic

D₉

—

C₂⁴

—

C₂⁴

C₂²×D₉

yes

characteristic

C₂×Q₈

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₄⋊C₄

—

106

C₂²⋊C₄

—

107

C₂²⋊C₄

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

#611

yes

—

110

C₂²×C₃

—

111

C₂²×C₃

—

112

C₂²×C₃

—

113

C₂²×C₃

#946

yes

—

114

C₂²×C₃

#947

yes

—

115

C₂²×C₃

#953

yes

characteristic

116

C₂×D₃

—

117

C₂×D₃

—

118

C₃×C₄

—

119

Dic₃

—

120

Dic₃

—

121

C₉

#2032

yes

characteristic, complemented, Sylow

122

C₂³

—

123

C₂³

—

124

C₂³

—

125

C₂³

Q₈×D₉

yes

characteristic

126

C₂³

#3701

yes

—

127

C₂³

C₂×#611

yes

—

128

Q₈

—

129

D₄

—

130

D₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₃

—

137

C₂×C₃

—

138

C₂×C₃

—

139

C₂×C₃

#5231

yes

characteristic

140

D₃

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

#63508

yes

—

147

C₂²

#63509

yes

—

148

C₂²

#63515

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

152

C₃

#71896

yes

characteristic

153

C₂

—

154

C₂

—

155

C₂

—

156

C₂

—

157

C₂

#10588911

yes

characteristic

	subgroup	G/H
center	C₂	#10588911
commutator, cosocle	C₂⁴×C₉	C₂³
Frattini	C₂⁴×C₃	C₂²×D₃
Fitting	C₉×#543	C₂
socle	C₂×C₃	#5231
prime radical	C₂²×#611	C₂²
hypercenter	#543	D₉
hypocenter	C₉	#2032
LCS	G ▷ C₂⁴×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #543

subgroup

G/H

center

C₂

#10588911

commutator, cosocle

C₂⁴×C₉

C₂³

Frattini

C₂⁴×C₃

C₂²×D₃

C₂

C₂×C₃

C₂²×#611

C₂²

D₉

C₉

G ▷ C₂⁴×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂ ◁ C₂⁴ ◁ #543

N	H ≅ G/N	type
1. C₉×#543	C₂	semidirect
3. #10588204	C₂	semidirect
14. C₂³×D₉	Q₈	semidirect
20. C₂²×Dic₉	Q₈	semidirect
46. #543	D₉	semidirect
121. C₉	#2032	semidirect

H ≅ G/N

type

1. C₉×#543

C₂

semidirect

3. #10588204

C₂

semidirect

14. C₂³×D₉

Q₈

semidirect

20. C₂²×Dic₉

Q₈

semidirect

46. #543

D₉

semidirect

121. C₉

#2032

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₉×#543	2
C₂×#63365	2
#10588204	2
#71896	3

subgroup

index

Subgroups — #11793125

Conjugacy classes of subgroups

Complements

Maximal subgroups